A guitar made out of Lego pieces was sold recently on eBay. Click here for the pictures. It is a tribute to the Gibson Les Paul, with a P90 in the bridge position and a humbucker at the neck. Apparently it is fully functional, but suffers from tuning instability due to the weakness of the neck.
This has the makings of a good idea. I would have started with a normal guitar neck attached to a small rudimentary body, something like the Steinberger headless/bodyless guitars. The body and headstock would have the Lego bumps all over them so you could customise the shape by adding more Lego pieces to it. You could then change the guitar's shape, colour and pickups depending on your moods.